The Two-Dimensional Clifford-Fourier Transform

Recently several generalizations to higher dimension of the Fourier transform using Clifford algebra have been introduced, including the Clifford-Fourier transform by the authors, defined as an operator exponential with a Clifford algebra-valued kernel. In this paper an overview is given of all these generalizations and an in depth study of the two-dimensional Clifford-Fourier transform of the authors is presented. In this special two-dimensional case a closed form for the integral kernel may be obtained, leading to further properties, both in the L ₁ and in the L ₂ context. Furthermore, based on this Clifford-Fourier transform Clifford-Gabor filters are introduced. AMS subject classification numbers: 42B10, 30G35 Fred Brackx received a diploma degree in mathematics from Ghent University, Belgium, in 1970 and a Ph.D. degree in mathematics from the same university in 1973. Since 1984 he is professor for mathematical analysis at Ghent University and currently he is leading the Clifford Research Group. His main interests are function theory and functional analysis for functions with values in quaternion and Clifford algebras. The research covers Clifford distributions, generalized Fourier, Radon and Hilbert transforms, orthogonal polynomials and multi-dimensional wavelets. Nele De Schepper received a diploma degree in mathematics from Ghent University, Belgium, in 2001. Since then she holds an assistantship at the Department of Mathematical Analysis of Ghent University and is a member of the Clifford Research Group. Her main interests are function theory and functional analysis for functions with values in Clifford algebras. The research covers generalized Fourier transforms, orthogonal polynomials and multi-dimensional wavelets. Frank Sommen received a diploma degree in mathematics from Ghent University, Belgium, in 1978, a Ph.D. degree in mathematics from the same university in 1980, and a habilitation degree in mathematical analysis in 1984. From 1978 until 1999 he was at the National Fund for Scientific Research (Flanders). Since 2000 he holds a Research professorship at Ghent University. His main interests are function theory and functional analysis for functions with values in quaternion and Clifford algebras. The research covers Clifford distributions, generalized Fourier, Radon and Hilbert transforms, orthogonal polynomials and multi-dimensional wavelets, algebraic analysis, hyperfunctions and radial algebra.     

Implementation of RNS-Based Distributed Arithmetic Discrete Wavelet Transform Architectures Using Field-Programmable Logic

Currently there are design barriers inhibiting the implementation of high-precision digital signal processing (DSP) objects with field programmable logic (FPL) devices. This paper explores overcoming these barriers by fusing together the popular distributed arithmetic (DA) method with the residue number system (RNS) for use in FPL-centric designs. The new design paradigm is studied in the context of a high-performance filter bank and a discrete wavelet transform (DWT). The proposed design paradigm is facilitated by a new RNS accumulator structure based on a carry save adder (CSA). The reported methodology also introduces a polyphase filter structure that results in a reduced look-up table (LUT) budget. The 2C-DA and RNS-DA are compared, in the context of a FPL implementation strategy, using a discrete wavelet transform (DWT) filter bank as a common design theme. The results show that the RNS-DA, compared to a traditional 2C-DA design, enjoys a performance advantage that increases with precision (wordlength).     

A unified framework for off-line permutation routing in parallel networks

In this paper we present a general strategy for finding efficient permutation routes in parallel networks. Among the popular parallel networks to which the strategy applies are mesh networks, hypercube networks, hypercube-derivative networks, ring networks, and star networks. The routes produced are generally congestion-free and take a number of routing steps that is within a small constant factor of the diameter of the network. Our basic strategy is derived from an algorithm that finds (in polynomial time) efficient permutation routes for aproduct network, G×H, given efficient permutation routes forG andH. We investigate the use of this algorithm for routingmultiple permutations and extend its applicability to a wide class of graphs, including several families ofCayley graphs. Finally, we show that our approach can be used to find efficient permutation routes among the remaining live nodes infaulty networks.This research was supported in part by a grant from the NSF, Grant No. CCR-88-12567.     

Finite-element grid improvement by minimization of stiffness matrix trace

A new and simple method of finite-element grid improvement is presented. The objective is to improve the accuracy of the analysis. The procedure is based on a minimization of the trace of the stiffness matrix. For a broad class of problems this minimization is seen to be equivalent to minimizing the potential energy. The method is illustrated with the classical tapered bar problem examined earlier by Prager and Masur. Identical results are obtained.     

Category Norms as a Function of Culture and Age: Comparisons of Item Responses to 105 Categories by American and Chinese Adults.

Understanding how aging influences cognition across different cultures has been hindered by a lack of standardized, cross-referenced verbal stimuli. This study introduces a database of such item-level stimuli for both younger and older adults, in China and the United States, and makes 3 distinct contributions. First, the authors specify which item categories generalize across age and/or cultural groups, rigorously quantifying differences among them. Second, they introduce novel, powerful methods to measure between-group differences in freely generated ranked data, the rank-ordered logit model and Hellinger Affinity. Finally, a broad archive of tested, cross-linguistic stimuli is now freely available to researchers: data, similarity measures, and all stimulus materials for 105 categories and 4 culture-by-age groups, comprising over 10,000 fully translated unique item responses. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Moving on and moving up: The experience of households who resell public sector dwellings

The long‐term consequences of the sale of public sector dwellings to sitting tenants are under‐researched; in particular, the experience of tenant purchasers in the housing market subsequent to purchase is little known. This paper reports research designed to fill this gap in knowledge. Over 200 tenants who had bought their dwelling from the Scottish Special Housing Association and subsequently resold on the open market were traced using the Register fo Sasines and the Land Register and interviewed. Most had made considerable capital gains on resale and had used some of the realised capital to trade up in the housing market. They were, on average, slightly more affluent and younger than sitting tenant purchasers generally; they represented a group of households who were privileged within the public sector through living as tenants in the best stock and who were enabled by the Right to Buy to convert that good luck into hard cash and move into mainstream owner occupation. This good luck compounded the advantaged position vis‐à‐vis other tenants that they enjoyed in the labour market.     

Vocal fatigue among teachers

Recordings were made at the beginning and end of workdays of teachers who experience vocal fatigue (n = 22) and those who do not experience fatigue (n = 17). Those who experienced fatigue were recorded on days in which they did and did not fatigue. Both groups evaluated their vocal characteristics, each time they made a recording. Subsequently, a listener panel evaluated the same characteristics from the recordings. Both groups estimated the amount and characteristics of their talking time, completed a psychological evaluation and provided medical histories. The authors interpret the data obtained as indicating that the vocal characteristics of teachers who fatigue and those who do not fatigue are similar on days the former group does not fatigue and that the two groups are similar in the amount and loudness of their talking time, at work and at home. However, teachers who fatigue tend to spend more time in activities that appear to be vocally demanding and are more likely to perceive situations as being anxiety producing. Teachers who fatigue tend to be in good health, but have had more hearing problems and allergies than their colleagues and more of their family members have had voice problems.     

FRACTURE ASSESSMENT FOR SECONDARY LOADS

The fracture assessment of structures subjected to secondary loading systems was studied by FEM-analysis of a few illustrative two-dimensional examples. The first example is an edge-cracked plate with a thermal gradient. The FEM-calculations revealed that a purely elastic analysis yielded J-values that are in most cases considerably more conservative than the ones calculated from an elastic-plastic analysis. The results were further compared with different engineering type non-linear estimates. As a second example a crack emanating from a semi-circular notch in a rectangular plate was chosen. The plate was subjected to uniaxial tension along its boundaries. It turned out that for the cases considered the J-values were fairly close to those elastically predicted.